Probability Hypergeometric Distribution

In this lesson, we are going to be discussing the glamorously named hypergeometric distribution. First you'll see the situation where you would use the hypergeometric distribution. Then you'll learn the definition: the hypergeometric distribution describes choosing a committee of n men and women from a larger group of r women and N-r men. This is an unordered choice, without replacement. There are a lot of parameters in the formula for this distribution, and once you understand them, it'll be easier for you to memorize the formula. We are also going to go over some key properties of the hypergeometric distribution.

I don't follow where you get each indicator variable to be equal to r/N.Y1 is OK but, surely, the probability of picking the gender of the second person depends on your first choice as there is no replacement. If the first choice is a woman then the probability of getting a woman on the second choice is (r-1)/(N-1) but if the first choice was a man then the probability of getting a woman is r/(N-1). The probability of picking a woman gets even more complex on the third choice as it depends on whether you have picked 2, 1 or 0 women already being (r-2)/(N-2), (r-1)/(N-2) and r/(N-2) respectively. This trend continues all the way up to the nth choice where depending on how many women have been picked already the probability of picking a woman is (r-n-1)/(N-n-1), ... (r-2)/(N-n-1), (r-1)/(N-n-1), r/(N-n-1).I can't see how this simplifies to nr/N.What am I missing?

Hypergeometric Distribution

Hypergeometric Distribution

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